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Condensed Matter Theory 1 (CMT1)

Course content

This course is an introduction to quantum field theoretical
methods aimed for both experimentalists and theorists with
particular focus on condensed matter physics. The content spans a
wide range of topics necessary for understanding concepts and
methods used in advanced solid state physics. Finally, the course
provides a good foundation for the course CMT2 and for doing active
research in condensed matter physics at the Niels Bohr
Institute.

In the course, we focus on the interacting electron gas,
describing metals and semiconductors, and use this as an example to
illustrate the techniques taught. The course is meant to teach
the fundamental filed-theoretical concepts and techniques such as
second quantization, equations of motion for operators,
many-particle Green functions at finite temperatures, and Feynman
diagrams.

Derive and use Feynman rules for perturbation theory within
potential scattering, electron-electron, and electron-phonon
interactions.

Perform a detailed calculation and regularization of the ground
state energy for the interacting electron gas including the
screening of long-range Coulomb interactions and its Landau damped
plasmons.

Describe single-particle excitations in an interacting
many-particle system in terms of renormalized quasi-particles. This
includes being able to obtain effective masse and charge, Fermi
surfaces, Z-factors and lifetimes.

To use all these acquired skills to solve relevant physics
problems, including mainly issues within the physics of solid
materials, nano-scopic systems, quantum liquids and ultracold
atomic gasses.

Knowledge
In the course, we focus on the interacting electron gas, describing
metals and semiconductors, and use this as an example to illustrate
the techniques taught. The course is meant to teach the fundamental
filed-theoretical concepts and techniques such as second
quantization, equations of motion for operators, many-particle
Green functions at finite temperatures, and Feynman diagrams.

Competences
This course will provide the students with the required background
for further studies within this research field, i.e. the course
CMT2 or a master thesis. The course will provide most of the modern
formalism used in the scientific literature on condensed matter
physics.